Specialization in Ocean Energy MODELLING OF WAVE ENERGY CONVERSION António F.O. Falcão Instituto Superior Técnico, Universidade de Lisboa 2017

MODELLING OF OWC WAVE ENERGY CONVERTERS PART 4 MODELLING OF OWC WAVE ENERGY CONVERTERS

Basic approaches to OWC modelling will be analized here

Basic equations Volume flow rate of air displaced by OWC motion Decompose into excitation flow rate radiation flow rate

air compressibility effect Basic equations air compressibility effect

Thermodynamics of air chamber Assume compression/decompression process in air chamber to be isentropic (adiabatic + reversible). This implies perfectly efficient air turbine.

Thermodynamics of air chamber Better approximation: real turbine with average efficiency h . Process is polytropic instead of isentropic, Replace exponent g by k Typical values for “good” air turbines: h = 0.6 to 0.7

X Aerodynamics of air turbine Dependence on Mach number Ma in general neglected, because of scarce information from model testing. X

Frequency domain analysis Linear turbine Linear relationship air density versus pressure Linearize: Wells turbine

Frequency domain analysis The system is linear Decompose Note: radiation conductance G cannot be negative

PICO OWC PLANT, AZORES, PORTUGAL

Frequency domain analysis (deep water) Axisymmetric body (deep water)

If the inner free surface is approximately flat, then there is a relationship between A, B, G, H, Fe and Qe

Frequency domain analysis Power Power available to turbine = pressure head x volume flow rate Regular waves Time average

Can be rewritten as: For given OWC and given incident regular waves, Qe and G are fixed.

Frequency domain analysis Power Turbine power output Wells turbine

Exercise Consider the Pico OWC plant. Air chamber volume V0 = 1050 m3 . Compute the average power absorbed from regular waves of period 10 s and amplitude 1.0 m. Compute approximately D and W for the Wells turbine Pico plant

Pico plant

Wells turbine with guide vanes

Turbine efficiency

Turbine power

Turbine flow rate versus pressure head

Time-domain analysis of OWCs The Wells turbine is approximately linear. So frequency-domain analysis is a good approximation. Other turbines (e.g. impulse turbines) are far from linear. So, time-domain analysis must be used, even in regular waves. This affects specially the radiation flow rate, with memory effects. The theoretical approach is similar to time-domain analysis of oscillating bodies.

radiation flow rate memory function

MODELLING OF OWC WAVE ENERGY CONVERTERS END OF PART 4 MODELLING OF OWC WAVE ENERGY CONVERTERS

Additional Exercise 5